Permutation of natural numbers induced by the automorphism gt-bf->df (switch from the Breadth First to the Depth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.

When restricted to the subset of plane binary trees, produces the automorphism A057117, with which this shares the property of "self-embeddability": each sub-permutation of the length A000108(n): 0; 1; 2,3; 4,5,6,7,8; 9,10,11,12,13,14,19,16,17,18,15,20,21,22; 23,24,25,26,27,28,33,30,31,32,29,34,35,36,37,51,38,56,60,42,47,44,45,46,53,48,49,50,39,41,43,54,61,40,57,58,59,52,55,62,63,64; starts with the same cycle-structure as the previous sub-permutation. (i.e. the terms from the first to the sixth are fixed, the 7th and 11th are transposed, etc.), thus allowing us to construct the permutation A072619 (A072621).